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This paper concerns a class of infinite horizon optimal control problems with state constraints. By extending the needle variation method to the infinite horizon case we obtain a complete set of necessary optimality conditions for a strong…

Optimization and Control · Mathematics 2020-07-21 Nico Tauchnitz

In this paper, we discuss the maximum principle for a time-fractional diffusion equation $$ \partial_t^\alpha u(x,t) = \sum_{i,j=1}^n \partial_i(a_{ij}(x)\partial_j u(x,t)) + c(x)u(x,t) + F(x,t),\ t>0,\ x \in \Omega \subset {\mathbb R}^n$$…

Analysis of PDEs · Mathematics 2021-03-12 Yuri Luchko , Masahiro Yamamoto

We develop a necessary stochastic maximum principle for a finite-dimensional stochastic control problem in infinite horizon under a polynomial growth and joint monotonicity assumption on the coefficients. The second assumption generalizes…

Probability · Mathematics 2017-03-14 Carlo Orrieri , Petr Veverka

We study the validity of the comparison and maximum principles, and their relation with principal eigenvalues, for a class of degenerate nonlinear operators that are extremal among operators with one dimensional fractional diffusion.

Analysis of PDEs · Mathematics 2021-07-16 Isabeau Birindelli , Giulio Galise , Delia Schiera

The famous proof of the Pontryagin maximum principle for control problems on a finite horizon bases on the needle variation technique, as well as the separability concept of cones created by disturbances of the trajectories. In this…

Optimization and Control · Mathematics 2018-07-05 Nico Tauchnitz

We prove a sufficient stochastic maximum principle for the optimal control of a regime-switching diffusion model. We show the connection to dynamic programming and we apply the result to a quadratic loss minimization problem, which can be…

Optimization and Control · Mathematics 2014-01-31 Catherine Donnelly

We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are…

Optimization and Control · Mathematics 2021-08-10 Faical Ndairou , Delfim F. M. Torres

A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…

Optimization and Control · Mathematics 2013-12-30 Kai Du , Qingxin Meng

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…

Probability · Mathematics 2008-07-23 Seid Bahlali

In this paper we prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a finite dimensional stochastic differential equation, driven by a multidimensional Wiener process. We drop the usual…

Optimization and Control · Mathematics 2017-03-14 Carlo Orrieri

In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first…

Optimization and Control · Mathematics 2021-01-18 Olivier Menoukeu-Pamen , Ludovic Tangpi

We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity…

Numerical Analysis · Mathematics 2017-04-05 Enrique Otárola , Abner J. Salgado

In this paper, we consider a diffusion equation with fractional-time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. Existence and uniqueness of solution are proved by means of a spectral argument. The existence of…

Analysis of PDEs · Mathematics 2017-11-27 J. D. Djida , G. M. Mophou , I. Area

A general stochastic maximum principle is proved for optimal controls of semilinear stochastic evolution equations. Stochastic evolution operators, and the control with values in a general set enter into both drift and diffusion terms.

Optimization and Control · Mathematics 2012-07-03 Kai Du , Qingxin Meng

In this paper we obtain new estimates of the sequential Caputo fractional derivatives of a function at its extremum points. We derive comparison principles for the linear fractional differential equations, and apply these principles to…

Analysis of PDEs · Mathematics 2021-06-15 Mokhtar Kirane , Berikbol T. Torebek

We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…

Optimization and Control · Mathematics 2021-10-08 Harbir Antil , Ciprian G. Gal , Mahamadi Warma

We obtain the variational equations for backward stochastic differential equations in recursive stochastic optimal control problems, and then get the maximum principle which is novel. The control domain need not be convex, and the generator…

Optimization and Control · Mathematics 2015-07-14 Mingshang Hu

In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…

Optimization and Control · Mathematics 2026-02-19 Javier de Frutos , Julia Novo

In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo…

Optimization and Control · Mathematics 2016-08-24 H. M. Ali , F. Lobo Pereira , S. M. A. Gama

We shall consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equations of the following type: d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt +…

Probability · Mathematics 2012-02-20 AbdulRahman Al-Hussein